Kershaw (11-7) allowed five hits and recorded six strikeouts for the Dodgers, who halted a two-game skid and won for only the second time in their last seven games overall.
Scott Podsednik and James Loney both drove in two runs. The Dodgers are seven games behind the Phillies in the NL wild card race.
Rockies starting pitcher Jhoulys Chacin (5-9) was recalled from Triple-A Colorado Springs earlier Tuesday and allowed five runs on five hits with four strikeouts and five walks over five innings of work.
Eric Young and Dexter Fowler had two hits for the inconsistent Rockies, who have alternated wins and losses throughout the month of August thus far.
Colorado is now six games off the pace in the wild card chase.